A few days ago
Related Rates Question?
A radio transmitter is located 3 km from a fairly straight section of interstate highway. A truck is traveling away from the transmitter along the highway at a speed of 80 km/h. How fast is the distance between the truck and the transmitter increasing when they are 5 km apart?
Please show how you got the answer. 10 points =)
Top 1 Answers
A few days ago
Favorite Answer
Always make a sketch of these things. Call the distance along the highway x. The distance from the highway is a constant 3 km. The distance between the truck and the transmitter, then, will be the hypotenuse of a right triangle with legs of 3km and x. You also know that dx/dt is +80 km/hr. (Note: Why is it +80 and not -80?) Let s be the distance from the truck to the antenna.
So:
x^2 + 3^2 = s^2
Implicitly differentiate:
2x dx/dt = 2s ds/dt
(Why does the 3^2 disappear?)
You’re looking for ds/dt, so solve:
ds/dt = (x/s) dx/dt
All you need to know now are the x and s distances at the point where you want to solve the problem. Since the problem says that the truck and transmitter are 5 km apart, you have s – you just need x. If you’ve made the sketch, it should be pretty clear how to find x, if you haven’t spotted it already.
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